How hot does the inside of a car get, and how fast? Check out this animation from the National Weather Service via the link. According to their information, the inside of a vehicle can reach 100 degrees in 25 minutes - and that's when it's only 73 degrees outside.
The atmosphere and the windows of a car are relatively transparent to the suns shortwave radiation (yellow in figure below) and are warmed little. This shortwave energy, however, does heat objects it strikes. For example, a dark dashboard or seat can easily reach temperatures in the range of 180 to more than 200 degrees F.